# Two-Variable Data: Models and Scatterplots on the SAT: Examples & Practice Source: https://1600.now/sat-skill/two-variable-data --- Math · Problem-Solving and Data Analysis ## Two-Variable Data: Models and Scatterplots A scatterplot compares paired variables. Read the direction and shape of the association, use a model to predict an output, and distinguish an observed value from that prediction. Written by [Luke Finigan](https://1600.now/about) 2 min read Updated Oct 2, 2026 ### Read a model's slope in the variables' units Suppose $\hat y=12+3x$ predicts plant height in centimeters from time in weeks. The slope predicts 3 more centimeters for each additional week. At week 5, the predicted height is $12+3(5)=27$ centimeters. The intercept predicts 12 centimeters at week zero. If zero is outside the observed range, that intercept is still part of the equation but may not describe a measured condition. ### Calculate residual as actual minus predicted If the observed height at week 5 is 25 centimeters, the residual is $25-27=-2$ centimeters. The point lies below the model because the prediction is too high by 2. Keep the order fixed. Predicted minus actual would reverse the sign. A residual of zero means the observation is exactly on the model, not that the height itself is zero. ### Match the model to the pattern A roughly straight cloud of points can support a linear model. A steadily changing ratio, such as outputs doubling over equal input intervals, suggests an exponential model. Curvature in the scatterplot gives a reason to question a straight-line fit. A strong association means the model follows the observed pattern closely. It does not establish that changing one variable causes the other to change; another variable could influence both. ### Limit predictions to what the data support A model built from measurements over weeks 1 through 8 predicts week 5 within its observed range. Predicting week 50 is extrapolation and needs an assumption that the same relationship continues. When a question asks which conclusion is supported, check both the direction of the association and the size of the claim. A model can estimate a value without guaranteeing that exact outcome for every observation. ### Check your understanding Try it yourself A model predicts $y=2x+5$. At $x=4$, the observed $y$ is 11. What is the residual? A $-2$ B $2$ C $11$ D $13$ Two-Variable Data: Models and Scatterplots · Worksheet question A line of best fit for a set of data is $y = 2.5x + 12$, where $x$ is the number of hours a student studied and $y$ is the student's quiz score. What quiz score does the line predict for a student who studied 6 hours? A 15 B 18 C 24 D 27 ### Practice this skill 1. Label both axes and the units of the slope. 2. Calculate a prediction and one residual by hand. 3. Identify whether each prediction is inside or outside the measured range. [Practice two-variable data: models and scatterplots](https://1600.now/bank/math/skill/Two-variable%20data%3A%20Models%20and%20scatterplots) [Print the two-variable data: models and scatterplots worksheet and worked answers](https://1600.now/sat-two-variable-data-worksheet). Then use a [mixed practice module](https://1600.now/modules) to check whether you can choose this method among other question types. ### Source and question labels The bank label for this guide is "Two-variable data: Models and scatterplots" in Problem-Solving and Data Analysis. The worked examples above are written for this guide. - [College Board: Types of Math tested](https://satsuite.collegeboard.org/sat/whats-on-the-test/math/types) ### Related skills - **[Linear Functions](https://1600.now/sat-skill/linear-functions)** A linear function changes by the same amount for each equal increase in its input. - **[Nonlinear Functions](https://1600.now/sat-skill/nonlinear-functions)** The form of a nonlinear function tells you what you can read directly. - **[Evaluating Statistical Claims](https://1600.now/sat-skill/evaluating-statistical-claims)** Check two separate permissions: random sampling supports generalizing to a population, while random assignment in a well-designed experiment supports a causal comparison.